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Propagators and dilations

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Probability Theory on Vector Spaces

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 656))

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References

  1. N. Aronszajn, La theorie generale de noyaux reproduisants et ses applications, Proc.Cambridge Philos. Soc. 39 (1944), 133–153.

    Article  MathSciNet  Google Scholar 

  2. N. Aronszajn, Theory of reproducing kernels, Trans.Amer. Math. Soc. 68 (1950), 337–404.

    Article  MathSciNet  MATH  Google Scholar 

  3. W. Arveson, Subalgebras of C*-algebras, Acta Math. 123 (1969), 141–224.

    Article  MathSciNet  MATH  Google Scholar 

  4. W. Arveson, Subalgebras of C*-algebras II, Acta Math. 128 (1972), 271–308.

    Article  MathSciNet  MATH  Google Scholar 

  5. J. Bram, Subnormal operators, Duke Math. J. 22 (1955), 75–94.

    Article  MathSciNet  MATH  Google Scholar 

  6. S.A. Chobanian, On a class of functions of a Banach space valued stationary stochastic process, Sakharth SSR Mecn. Acad.Moambe 55 (1969), 21–24.

    Google Scholar 

  7. R.K. Getoor, The shift operator for non-stationary stochastic processes, Duke Math. J. 23 (1956), 175–187.

    Article  MathSciNet  MATH  Google Scholar 

  8. J. Hadamard: Lectures on Cauchy's Problem in linear differential equations, Dover Publications, New York, 1952.

    MATH  Google Scholar 

  9. P.R. Halmos, Normal dilations and extensions of operators, Summa Brasiliensis Math. 2 (1950), 125–134.

    MathSciNet  Google Scholar 

  10. P.R. Halmos, A Hilbert space problem book, van Nostrand, New York, 1967.

    MATH  Google Scholar 

  11. E. Hille and R.S. Phillips, Functional analysis and semigroups, Amer. Math. Soc. Colloq. Publ., Vol. 31, Amer. Math. Soc., Providence, R.I., 1957.

    MATH  Google Scholar 

  12. K. Karhunen, Uber lineare Methoden in der Wahrscheinlichkeitsrechnung, Ann. Acad. Sci. Fenn. Ser. A.1 37 (1947)

    Google Scholar 

  13. A.N. Kolmogorov, Stationary sequences in Hilbert space, Bull. Math. Univ. Moscow 2 (1941), 1–40.

    Google Scholar 

  14. A. Lebow, On von Neumann's theory of spectral sets, J. Math. Anal. & Appl. 7 (1963), 64–90.

    Article  MathSciNet  MATH  Google Scholar 

  15. V. Mandrekar & H. Salehi, The square-integrability of operator-valued functions with respect to a non-negative operator-valued measure and the Kolmogorov isomorphism theorem, Indiana Univ. Math. J. 20 (1970), 545–563.

    Article  MathSciNet  MATH  Google Scholar 

  16. P. Masani, Orthogonally scattered measures, Adv. in Math. 2 (1968), 61–117.

    Article  MathSciNet  MATH  Google Scholar 

  17. P. Masani, Quasi-isometric measures and their applications, Bull. Amer. Math. Soc. 76 (1970), 427–528.

    Article  MathSciNet  MATH  Google Scholar 

  18. P. Masani, Dilations as propagators of Hilbertian varieties, S.I.A.M. J Anal. 9 (1978) to appear.

    Google Scholar 

  19. W. Mlak, Operator inequalities and related dilations, Acta Sci. Math., 34 (1973),273–278.

    MathSciNet  MATH  Google Scholar 

  20. W. Mlak, Dilations of Hilbert space operators (General Theory) to appear in Dissertationes Math. 158.

    Google Scholar 

  21. B. Sz.-Nagy, Extensions of linear transformations in Hilbert space which extend beyond this space, F. Ungar, New York, 1960. (German Ed. Deutscher Verlag der Wissenchaften Berlin, 1950).

    Google Scholar 

  22. B. Sz,-Nagy & C. Foias, Harmonic analysis of operators on Hilbert space, North Holland, New York, 1970.

    MATH  Google Scholar 

  23. G.B. Pedrick, Theory of reproducing kernels in Hilbert spaces of vector valued functions, Univ. of Kansas Technical Report 19 (1957).

    Google Scholar 

  24. R. Shonkwiler, On generalized resolvents and an integral representation of Nevanlinna, J. Math. Anal. & Appl. 40 (1972), 723–734.

    Article  MathSciNet  MATH  Google Scholar 

  25. R. Shonkwiler & G. Faulkner, Kernel dilation in reproducing kernel Hilbert space and its applications to moment problems (to appear).

    Google Scholar 

  26. W. Stinespring, Positive functions on C*-algebras, Proc.Amer. Math. Soc. 6(1955), 211–216.

    MathSciNet  MATH  Google Scholar 

  27. F.H. Szafraniec, Dilations on involution semi-groups Proc. Amer. Math. Soc. (to appear).

    Google Scholar 

  28. N.N. Vakhania, The covariance of random elements in a Banach space, Thbilis Sanelme. Univ. Gamoqeneb. Math. Inst.2 (1969) 179–184.

    Google Scholar 

  29. J. von Neuman & I.J. Schoenberg, Fourier integrals and metric geometry, Trans. Amer. Math. Soc. 50 (1941), 226–251.

    Article  MathSciNet  MATH  Google Scholar 

  30. A. Weron, Remarks on positive definite operator valued functions in Banach Spaces, Bull. Acad. Polonaise Sci. 24 (1976), 873–876.

    MathSciNet  MATH  Google Scholar 

  31. A. Weron and J. Górniak, An analogue of Sz.-Nagy's dilation theorem, Bull. Acad. Polonaise Sci. 24 (1976), 867–872.

    MATH  Google Scholar 

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Authors and Affiliations

  1. University of Pittsburgh, 15260, Pittsburgh, Pa, USA

    P. Masani

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  1. P. Masani
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A. Weron

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© 1978 Springer-Verlag

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Masani, P. (1978). Propagators and dilations. In: Weron, A. (eds) Probability Theory on Vector Spaces. Lecture Notes in Mathematics, vol 656. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0068814

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  • DOI: https://doi.org/10.1007/BFb0068814

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08846-2

  • Online ISBN: 978-3-540-35814-5

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